Detection of Ordered and Chaotic Motion Using the Dynamical Spectra |
| |
Authors: | N Voglis G Contopoulos C Efthymiopoulos |
| |
Institution: | (1) Department of Astronomy, University of Athens, Greece;(2) Department of Astronomy, University of Athens, Greece |
| |
Abstract: | Two simple and efficient numerical methods to explore the phase space structure are presented, based on the properties of
the "dynamical spectra". 1) We calculate a "spectral distance" D of the dynamical spectra for two different initial deviation
vectors. D → 0 in the case of chaotic orbits, while D → const ≠ 0 in the case of ordered orbits. This method is by orders
of magnitude faster than the method of the Lyapunov Characteristic Number (LCN). 2) We define a sensitive indicator called
ROTOR (ROtational TOri Recongnizer) for 2D maps. The ROTOR remains zero in time on a rotational torus, while it tends to infinity
at a rate ∝ N = number of iterations, in any case other than a rotational torus. We use this method to locate the last KAM
torus of an island of stability, as well as the most important cantori causing stickiness near it.
This revised version was published online in July 2006 with corrections to the Cover Date. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|